Inversion Method for Reconstructing Hall Thruster Plume Parameters from the Line Integrated Measurements (Postprint)

摘要

Utilizing symmetry and extensive datasets, it is possible to extract three-dimensional distributions from two dimensional data. Numerically, these inversions are unstable and prone to magnify noise. However, noise amplification can be controlled by careful addition of artificial smoothing within the numerical inversion algorithm. The precept of Tikhonov regularization is that a unique, stable solution to a deconvolution may be achieved by minimizing a constrained smoothing function. Fundamentally, this will generate a stable, single valued solution only so long as the uncertainty of the iterated solution does not exceed the uncertainty (noise) of the original data. Within these constraints, the algorithm is relatively insensitive to noise. Using Tikhonov deconvolution, it is possible to determine radial profiles from line integrated measurements. A preliminary evaluation of the deconvolution scheme was made with a biased tungsten wire acting as a Faraday probe. After the deconvolution method was assessed, it was applied to a spectroscopic survey of relative xenon neutral line intensities in the near infrared. The radially resolved emission ratios provide a three-dimensional estimate of the plume electron temperature using a published xenon collisional radiative model.